Interior-Point Methods for Nonlinear Optimization and Complementarity

建议#0098040普林斯顿大学Vanderbei，Robert J.优化是确定某些可控参数值的过程，以便在可行参数设置的指定域内实现目标函数的最佳值，即最小或最大值。 随着现代优化技术在解决现实问题方面的能力越来越被广泛认可，对高性能优化算法和软件的需求也在迅速增长。现代优化技术的成功很大程度上源于最近发展的所谓的边界点方法。 这些方法最初是为线性优化问题开发的，但现在正在积极地扩展到非线性优化问题。这项研究涉及到大规模非线性约束优化的新的边界点算法和软件的开发。 具体目标包括：（1）对现有技术的根本改进，例如用基于滤波器的方法取代步长控制的价值函数，以及开发更好的技术来检测无界和不可行的问题;（2）将基本算法推广到二阶锥规划和半定规划等新的问题类，（3）进一步扩展到非线性互补问题，这类问题在许多工程问题中出现;最后（4）开发一个大型的优化模型库，它既可以说明现代优化技术的力量，也可以为未来的算法开发提供一个测试平台。

Proposal #0098040Princeton UniversityVanderbei, Robert J.Optimization is the process of determining values of certain controllable parameters so as to achieve the best, i.e. smallest or largest, value of an objective function within a specified domain of feasible parameter settings. The demand for high-performance optimization algorithms and software is increasing rapidly as the power of the current technology to solve difficult real-world problems is becoming more widely recognized.Much of the success of modern optimization techiques stems from the recent development of so-called interior-point methods. These methods were first developed for linear optimization problems but are now actively being extended to nonlinear optimization problems.This research involves the development of new interior-point algorithms and software for large-scale nonlinear constrained optimization. Specific goals include: (1) fundamental enhancements to the current state-of-the-art, such as the replacement of the merit-function for step-length control with afilter-based method and the development of better techniques to detect unbounded and infeasible problems; (2) extension of the basic algorithm to new problem classes, such as second-order cone programming and semidefinite programming, that don't quite fit the basic paradigm of nonlinear constrained optimization; (3) further extension beyond the realm of optimization to nonlinear complementarity problems, which arise in many engineering problems; and finally (4) development of a large repository of optimization models, which serves both to illustrate the power of modern optimization technology and also to provide a test bed for future algorithm development.